Algorithm for Simple Automated Breast MRI Deformation Modelling
Marta Danch-Wierzchowska, Damian Borys and Andrzej Swierniak
Institute of Automatic Control, Silesian University of Technology, Akademicka 16, 44-100 Gliwice, Poland
Keywords:
Breast Deformation, Finite Element Modeling, MRI Images.
Abstract:
Increasing incidence of breast cancer caused development of patient-specific treatment planning procedures.
The most effective tool for breast cancer visualisation is Magnetic Resonance Imaging (MRI). However, the
MRI scans represent patient data in prone position with breast placed in signal enhancement coils, while other
procedures, i.e. surgery, PET-CT (Positron Emission Tomography fused with Computer Tomography) are
performed in patient supine position. The bigger patient breast is, the bigger its shape differ in every patient
position, what influences its interior structure and tumour location. In this paper, we present our method for
automated breast model deformation, which is based on prone MRI dataset. Proposed algorithm allows to
obtain reliable breast model in supine position in a few simple steps, without manual intervention.
1 INTRODUCTION
Recent studies show that breast cancer is the most
frequent women’s cancer around the world and it is
the second most frequent among all human cancers.
Due to that, diagnosis needs to be precise and fast,
whereas treatment needs to be as personalised as pos-
sible. Therefore, breast tissue deformation has re-
cently gained interest in various medical applications.
Considering specific anatomy of the female breast any
examination or intervention results in breast defor-
mation. For that reason, on every examinated image
set the tumour in question is placed in different area.
Moreover, female breast is very complex and irreg-
ular structure, consists of glandular lobules, adipose,
milk ducts, connective tissues and skin. It is impossi-
ble to model glandular lobules and milk ducts as sep-
arate layers, since it is almost impossible to differenti-
ate them on the MRI (Magnetic Resonance Imaging).
Due to that, breast is usually modeled as four lay-
ers: fibroglandular, fat, skin and muscle (Han et al.,
2012). In case of breast deformation modelling ge-
ometric transformation are mainly used for rigid and
minor non-rigid deformation (i.e. respiratory move-
ments) (Rueckert et al., 1999). To model major non-
rigid deformation (i.e. mammography compression or
prone to supine movement) knowledge-based trans-
formation inspired by biomechanical models is used.
FEM (Finite Element Modeling) is a numerical tech-
nique and, the same, allows approximate solving of
partial differential equations (PDE), which simplifies
computations. The main motivation of biomechanical
FEM models usage is that more information enables
reliable estimation of complex deformation (Lee
et al., 2010).
There are several applications of biomechanical
breast modelling. Almost all of them are related
to breast cancer diagnostics and treatment. The
oldest praxis is a mammography simulation which
presents the breast deformation caused by the plates
compression (Han et al., 2012), (Pathmanathan et al.,
2008). Another, more recent, application is breast
deformation caused by the gravitational force. Such
simulation is commonly used when different breasts
shapes comparison is needed, e.g. MRI compared
with PET-CT (Han et al., 2014). Fusion of different
examinations helps with more accurate diagnosis
(Abreu et al., 2013). Breast shape simulation in
different patient positions is used in treatment plan-
ning and tumour location during medical procedures,
e.g. surgery, biopsy procedure (Azar et al., 2000).
Already published studies concentrate on creating
one breast model based on patient or phantom data
and its deformation with one or few methods. The
results presented are very precise, but methodology
impossible to be applied in a broader spectrum.
Different modalities of breast imaging are carried out
in different patient positions. Especially, MRI imag-
ing, the most powerful method nowadays, is acquired
in patients lying in prone body position, with the
breast hanging down into the coil. However, majority
of therapeutic procedures, like surgery or radiation
114
Danch-Wierzchowska, M., Borys, D. and Swierniak, A.
Algorithm for Simple Automated Breast MRI Deformation Modelling.
DOI: 10.5220/0006586201140119
In Proceedings of the 11th International Joint Conference on Biomedical Engineering Systems and Technologies (BIOSTEC 2018) - Volume 2: BIOIMAGING, pages 114-119
ISBN: 978-989-758-278-3
Copyright © 2018 by SCITEPRESS Science and Technology Publications, Lda. All rights reserved
therapy are carried out in supine body position, with
significant displacement of breast tissue. Thus, the
simple method of breast deformation modelling will
be of clinical use, even if it is expected that the error
of this modelling will not allow for ideal transposition
of image. However, even rough transformation gives
better estimation of tissue relationships than the
routinely carried out visual assessment, regularly
used in the clinic.
There appear some limitations that cause inaccu-
racies of the created models. The main issue is
accurate tissue parameter estimation. Biomechanical
properties of breast tissues have been measured ex
vivo (A.Samani et al., 2007), (Wellman et al., 1999).
However living tissues have different properties than
those, extracted from body without blood circulation.
Moreover existing in vivo measuring methods (i.e.
elastography) do not provide information precise
enough to estimate big deformation (Insana et al.,
2005). Another issue is accurate mesh selection.
Different types of mesh elements and different mesh
node density give different results (Samani et al.,
2001) and in some cases the FE mesh requires man-
ual intervention (Han et al., 2012) as well as image
segmentation (Han et al., 2014), (Pathmanathan
et al., 2008). Further difficulty provides boundary
conditions setting, especially on chest wall side,
where the model ends but the real body consistency
needs to be preserved (Tanner et al., 2002). Still
unsolved modelling issue remains patient-specific,
fully-automated image deformation algorithm, which
is essential in clinical practice.
In this paper we present a basic idea of a simple
breast model and its deformation, paying a special
attention to further use in clinical practice. Pre-
sented paper is an extension to our previous work
described in (Danch-Wierzchowska et al., 2016b).
More precisely, previously presented algorithm was
extended to 3D, so that image dataset is processed
as one 3D object, instead of processing images one
by one separately. The algorithm itself was mod-
ified to eliminate issues, that were not significant,
nor present in 2D model. The biggest challenges
were to determine dependencies between nodes and
set model’s boundary conditions and to preserve
computational-time efficiency, while processing
significantly bigger number of nodes, than in 2D
analysis. In our work, we concentrated on simple and
efficient way to model breast deformation, that would
help with breast cancer diagnosis and could be used
in clinical practice.
Figure 1: Exemplary breast MR image (internal green con-
tour is a chestwall boundary, external green contour is a
body boundary).
2 MATERIAL AND METHODS
2.1 Breast MRI Data Acquisition
MRI is widely used in medical diagnosis, in partic-
ular breast imaging (Behrens et al., 2007). It is safe
technique because the MRI does not use the ioniz-
ing radiation. The possibility of multiple contrasts
acquisitions, both anatomical and functional, plays a
key role in MRI breast cancer detection. In this work
we use T1-weighted MRI scans, which were acquired
at the Center of Oncology ... with a Siemens scan-
ner. The data consist of 50 axial slices of patient in
prone position covering the area of interest. Obtained
data cover approximately 0.7x0.7x3 mm real volume
per voxel. Exemplary image, with Region of Inter-
est (ROI) outlined is shown in the Figure 1. The ob-
tained MRI data constitutes basis for FEM construc-
tion. This method requires domain (image set) dis-
cretisation, tissue parameter estimation, transforma-
tion equation definition, boundary condition setting
(see 2.2).
2.2 Deformation Algorithm
Deformation algorithm consist of a few main steps
based on FEM best practices and is fully implemented
in MATLAB.
Breast Segmentation. To obtain breast mask based
on MRI image, a fuzzy c-means algorithm is used
(Wu et al., 2013). However, after segmentation, man-
ual correction is needed. The breast mask used in our
algorithm is based on ROI presented in the Figure 1,
but to the point of a widest diameter of a patient chest.
Exemplary image mask is presented in the Figure 2.
Dividing into Left/Right Part. To shorten compu-
tational time, the model is divided into left and right
Algorithm for Simple Automated Breast MRI Deformation Modelling
115
Figure 2: Exemplary breast MR image mask.
Figure 3: Exemplary resulting mesh for image set (one
point represents one mesh node).
breast, which are joined in one model after deforma-
tion. Since there is no difference in methodology we
present only one half of the model.
Mesh Generation. Mesh generation is a process
where the coordinates of object domain nodes are set.
In case of breast MRI transformation the mesh gen-
eration is performed in two steps: (1) - generating
equidistant mesh for whole image set - domain vol-
ume, (2) - choosing nodes, which overlap a segmented
images mask. The resulting mesh is presented in the
Figure 3. For more details about mesh type see 4.
Finding Boundary Nodes. To set different param-
eters, the created model is divided into three parts
(See Figure 4): skin nodes, chestwall nodes and other
(fat and fibroglandular as one type) nodes. Boundary
nodes are set using neighborhood dependencies and
spatial localization.
Setting Nodes Parameters. Tissue parameters
were set according to (Azar et al., 2002) as isotropic,
homogeneous and incompressible material. Since the
data was obtained from patients at age 50-70 with
relatively big breast, it is justifiable to use simplifi-
cation of the breast model based on assumption, that
fat material parameters have much more influence on
Figure 4: Boundary conditions for mesh, chestwall nodes
(red), skin nodes (green).
deformation than fibroglandular ones (Pathmanathan
et al., 2008). Skin nodes constrain collision detection
and reaction. Chestwall nodes are set as stationary.
However, their material parameters are set, to sim-
ulate breast tissues sliding along muscles. Material
parameters used in the algorithm are presented in the
Table 1.
Table 1: Model parameters.
Node type Young Modulus Poission’s ratio
Skin 101 kPa 0.4995
Chestwall 5 kPa 0.1
Other 50 kPa 0.48
Incorporation of Gravitational Force. To imple-
ment deformation model (Azar et al., 2002) simplified
Lagrange equation of motion was used. The gravita-
tional force is applied to every node (except chestwall
nodes) in the mesh. Displacement of each node is iter-
atively calculated according to implemented equation
of motion. For more details see 4.
The incorporation of the gravitational force in the
model is performed in two steps: (1) Removal of the
gravitational force resulting from prone patient posi-
tion, (2) Application of gravitational force resulting
from supine patient position.
3 RESULTS
The exemplary deformation result is presented as
breast mesh in the supine plan. Figure 5 shows se-
lected mesh stages for an image set. The left image
is the original mesh, the middle is stage (1) of de-
formation - unload model (See 2.2), while the right
image contains the resulting mesh in supine patient
position. The resulting mesh was compared with AN-
SYS model created for the same patient in our pre-
vious work (Danch-Wierzchowska et al., 2016a) (See
BIOIMAGING 2018 - 5th International Conference on Bioimaging
116
Figure 5: Selected mesh deformation stages: original mesh
(upper left), unload mesh (upper right), resulting mesh (bot-
tom), (green - skin nodes, red - stiffened nodes, blue - other
nodes).
Figure 6: Reference ANSYS model (Danch-Wierzchowska
et al., 2016a).
Figure 6). Differences are easily visible. However,
the main shape is preserved.
Presented results are obtained in less than 30 min
per dataset on average portable computer, with mostly
automated algorithm. The only part, that requires
manual correction and extend computation time is
the image segmentation. This allows us to believe,
that our algorithm, optimised and improved, would
be useful in clinical practice.
4 DISCUSSION AND
CONCLUSIONS
It is clear that results obtained could not be precise.
There are many more conditions influencing tissue
movement than the gravitational force. There is still
muscle tension, which influences breast shape. It
is impossible to mimic all body dependencies and
movements personalized for every patient in limited
time. However, there are image processing algo-
rithms, like free-form deformation (FFD), which were
successfully used for small non-linear deformation
(Rueckert et al., 1999). The FFD algorithm could help
with a precise fitting of MRI image to supine refer-
ence image. Such images are obtained during PET-
CT for example, which is also common practice in
breast cancer diagnosis. Unfortunately, FFD is ineffi-
cient for large image deformations and cannot be used
as the only deformation tool.
In our previous work we have presented two differ-
ent approaches to breast deformation modelling. In
(Danch-Wierzchowska et al., 2016a) we created a
simplified woman’s chest model and simulate prone
to supine position changing in ANSYS. This work
was focused on tumour displacement while patient
position changing. The modelling error of tumour
displacement was less than 2 cm for approx. 1cm
tumour diameter and the results were deemed useful
by collaborating physicians. However, working with
ANSYS required too much effort to be used in ev-
eryday clinical practice. Moreover, costs of license
and training are to expensive for average medical unit.
Our second approach (Danch-Wierzchowska et al.,
2016b) was based on one image deformation, i.e. only
2D deformation model was required. Obtained results
were comparable with the result obtained with AN-
SYS model. The 2D results were compared with ref-
erenced, cross-section images from ANSYS model.
The 3D algorithm presented in this paper eliminate
the main cause of inaccuracy in 2D modelling by
adding movement in anteroposterior axis and main-
tains tissue continuity in every direction. Neverthe-
less it is not free from inaccuracy yet and needs fur-
ther improvement.
Modelling of breast deformation is mainly focused
on the impact of gravitational force on the breast
shape. One of the main challenges is a compromise
between model accuracy and efficiency. Complex tis-
sue models, represent every type of tissue, present in
the breast as separate layer (Han et al., 2012), could
never be used in clinical practice, since adapting them
to each patient would be too time-consuming. To
represent real breast movement several types of con-
stitutive models was created. Most popular way to
describe stress-strain relationship for fat and glandu-
lar tissue is the hyperelastic neo-Hookean constitutive
model (Hopp et al., 2012). Analysis using available
commercial software (i.e. ANSYS) gives acceptable
results and allows to use complex constitutive tissue
models, but implementing a body geometry inside it
is still highly time-consuming (Danch-Wierzchowska
et al., 2016a), (Han et al., 2012). The best solution
would be to create a fully automated algorithm, which
build geometry based directly on medical images and
deform it, without using any third-party software, es-
pecially when using it requires manual cooperation.
The model should be based only on breast essential
Algorithm for Simple Automated Breast MRI Deformation Modelling
117
structures chosen as an compromise between accu-
racy and efficiency. Developing a fully-automated
tool for creating a simplified model and incorporating
gravitational force will speed up the image analysis
significantly, along with time of diagnosis.
Our results show, that it is possible to create a sim-
ple model and in a few steps to deform it in a way
useful for treatment planning. Our main goal was
to mimic body displacement in the smallest possi-
ble number of steps with automated procedure, and
it is clear that the results obtained have a limited pre-
cision. We concluded, that there is no need to use
more sophisticated tissue constitutive model. Since
the simplest one gives acceptable results, preserving
computational efficiency, there is no purpose in com-
plicating the model. At the moment the methodology
does not require exact numerical Performance Index,
since the shape differences are easily visible. How-
ever, with such simple tissue model and simple defor-
mation equation, the results are promising.
Improving the deformation algorithm, creating MRI
images from obtained deformed mesh and proper seg-
mentation methods will be under further investigation
of our work.
ACKNOWLEDGEMENTS
This work was supported by the Polish Na-
tional Center of Research and Development grant
no. STRATEGMED2/267398/4/NCBR/2015 (MILE-
STONE - Molecular diagnostics and imaging in in-
dividualized therapy for breast, thyroid and prostate
cancer) (AS, DB) and the Institute of Automatic Con-
trol, Silesian University of Technology under Grant
No. BKM-508/RAU1/2017/t.1 (MDW).
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APPENDIX
Discretisation of the Domain
First step in the finite element analysis is object
domain discretisation - division into smaller domain
elements. It replaces the body with infinite degrees
of freedom by a finite number of elements with finite
and strictly defined degrees of freedom.
For three dimensional analysis one can discriminate
two main type of elements: four node tetrahedral el-
ement (T4) and eight node hexahedral element (Q8).
In this paper we focus on Q8 - linear brick element.
The Q8 element described in local coordinates (ξ, η,
µ) is presented below. (See Figure 7).
Figure 7: Linear brick element in local coordinates (Kattan,
2008).
Basic Equations in FEM Elastic
Deformation
The linear brick element is described by eight shape
functions listed as follows in terms of local ξ, η and µ
coordinates:
N
1
=
1
8
(1 ξ)(1 η)(1 +µ),
N
2
=
1
8
(1 ξ)(1 η)(1 µ),
N
3
=
1
8
(1 ξ)(1 + η)(1 µ),
N
4
=
1
8
(1 ξ)(1 + η)(1 + µ),
N
5
=
1
8
(1 + ξ)(1 η)(1 + µ),
N
6
=
1
8
(1 + ξ)(1 η)(1 µ),
N
7
=
1
8
(1 + ξ)(1 + η)(1 µ),
N
8
=
1
8
(1 + ξ)(1 + η)(1 + µ),
(1)
The strain displacement matrix is described as fol-
lows:
B =
1
|J|
[B
1
B
2
B
3
B
4
B
5
B
6
B
7
B
8
],
(2)
Table 2: Point coordinates and weights for two points
Gauss-Legendre quadrature.
n ξ
i
= η
i
= µ
i
W
i
2 ξ
1
= ξ
2
= ξ
3
= ±0.577350269189626 W
1
= W
2
= W
3
= 1
where J is the Jacobian determinant and the nodal B
i
matrix is given by:
B
i
=
N
i
x
0 0
0
N
i
y
0
0 0
N
i
z
N
i
y
N
i
x
0
0
N
i
z
N
i
y
N
i
z
0
N
i
x
. (3)
Element plane strain matrix is given as follows:
D =
E
(1+ν)(12ν)
1 ν ν ν 0 0 0
ν 1 ν ν 0 0 0
ν ν 1 ν 0 0 0
0 0 0
12ν
2
0 0
0 0 0 0
12ν
2
0
0 0 0 0 0
12ν
2
. (4)
with Young Modulus E and Poisson’s ratio ν.
The element stiffness matrix is given by:
k =
R
1
1
R
1
1
R
1
1
B
T
DBJdξdηdµ.
(5)
Two points Gauss-Legendre quadrature (Golub and
Welsch, 1969) is used for practical evaluation of in-
tegrals (5) over the element volume. The point coor-
dinates and weights are presented in the Table 2.
To calculate nodal displacement the following struc-
tural equation is used:
U = FK
1
,
(6)
where U is a node displacement matrix, F is nodal
forces matrix and K is a global stiffness matrix. Once
the boundary conditions are set, matrix U is solved
by partitioning and Gaussian elimination. For more
details see (Kattan, 2008).
Algorithm for Simple Automated Breast MRI Deformation Modelling
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